1. Field of the Invention
The present invention relates to a method for measuring the viscosity of a green compact sample formed by compaction molding of crystallized glass powder and the like, an apparatus for measuring the viscosity of a green compact sample, and a computer readable recording medium for storing the method for measuring the viscosity of the green compact sample.
Furthermore, the present invention relates to a method for measuring the viscosity of a green compact sample formed by compaction molding of amorphous glass powder and the like.
2. Description of the Related Art
Recently, in the electronics industry, various researches and developments have been made on ceramic multilayered substrates and thick-film materials which can meet higher densities for mounting components and circuit conductors, higher signal frequencies, etc. In particular, ceramic multilayered substrates which are formed by firing composite materials containing amorphous glass powder and crystallized glass can satisfactorily meet the higher density and higher frequency requirements because they have small relative dielectric constants and they can be fired simultaneously with Ag conductive materials having small resistivity.
In such ceramic multilayered substrates and thick-film materials, physical properties of inorganic oxide powder, such as amorphous glass powder and crystallized glass powder, strongly affect the substrate characteristics and thick-film characteristics. In particular, the viscosity characteristics thereof greatly affect the sintering process of the inorganic oxide powder, the diffusion behavior of Ag conductive materials, and so on, thus being significantly important parameters in material design and process design.
In general, in order to measure the viscosity of such glass powders, an extended fiber viscometer is used in the high viscosity region of approximately 1010Paxc2x7s or more, and a rotary viscometer (draw sphere viscometer) is used in the low viscosity region of approximately 104Paxc2x7s or less. The viscosity is measured by a parallel plate viscometer in the intermediate viscosity region of 104 to 109Paxc2x7s, which is particularly important in the sintering process of such glass powders.
A method for measuring viscosity xcex7 by a parallel plate viscometer will be described below.
First, as shown in FIG. 31, a test piece (sample) 1 in which the height H and the volume V have been accurately measured is placed on a quartz plate 2a which is fixed on a support 3. The test piece 1 is then sandwiched between the quartz plate 2a and a quartz plate 2b which is fixed to a quartz rod 4, and while a certain load M is applied to the quartz rod 4 and an apparatus 6 is heated by a heater 5, the displacement (height H) of the test piece 1 is detected by a differential transducer (not shown in the drawing) interlocking the quartz rod 4. By extracting the displacement over time, a sample deformation rate dh/dt of the test piece 1 is calculated.
Next, the sample volume V, the load M, and the sample deformation rate dh/dt are substituted into the Gent equation below to calculate the viscosity xcex7 of the test piece 1(refer to A. N. Gent, British Journal of Applied Physics, Vol. 11, Feb. 1960).
xcex7=2xcfx80MGH5/{3V(dh/dt)(2xcfx80H3+V)}
where M is the load, H is the height of the sample, G is the gravitational acceleration, V is the sample volume, and dh/dt is the sample deformation rate.
By performing the above for each temperature, and a variation of viscosity xcex7 with temperature, that is a viscosity-temperature curve is derived.
However, in the measurement of viscosity by the parallel plate viscometer described above, a bulk sample must be used as the test piece 1. That is, the Gent equation is only applicable in a case where the test piece 1 can be assumed to be an incompressible fluid. For example, when the viscosity of glass powder is measured, a bulk sample in which the glass powder is melted, quenched, and formed into a bulk material must be used.
That is, in the method described above, although the viscosity of glass which is formed into a bulk can be measured, it is difficult to measure the viscosity of glass in the powder state, in particular, the viscosity of crystallized glass powder. This is because of the fact that in the crystallized glass powder which tends to be crystallized, crystals may be precipitated during the formation of a bulk sample. Even if a bulk sample is formed, since the crystallization behavior is essentially different between the bulk sample and the powder sample, the viscous behavior differs between the bulk sample and the powder sample even with respect to the same type of glass powder.
However, as described above, in most of the ceramic multilayered substrates and thick-film materials, crystallized glass, amorphous glass, and the like are used as powder samples. That is, in view of material design and process design, evaluation of viscosity characteristics as powder samples must be performed with respect to crystallized glass, amorphous glass, and the like.
Accordingly, it is an object of the present invention to provide a method for measuring the viscosity of a green compact sample formed by compaction molding of inorganic powder with high accuracy. It is another object of the present invention to provide an apparatus for efficiently measuring the viscosity of a green compact sample. It is another object of the present invention to provide a computer readable recording medium for storing the method for measuring the viscosity of the green compact sample.
In one aspect of the present invention, in a method for measuring the viscosity of a green compact sample, the viscosity xcex7 of a green compact sample formed by compaction molding of inorganic powder is measured in accordance with the Gent equation:
xcex7=2xcfx80MGH5/{3V(dh/dt)(2xcfx80H3+V)}
where M is the load, H is the height of the sample, G is the gravitational acceleration, V is the sample volume, and dh/dt is the sample deformation rate.
The method includes the steps of:
(A) finding a corrected value Vxe2x80x2 of the sample volume of the green compact sample, where the corrected value Vxe2x80x2 of the sample volume is a volume occupied by the inorganic powder in the green compact sample;
(B) finding a corrected value (dh/dt)xe2x80x2 of the sample deformation rate of the green compact sample, where the corrected value (dh/dt)xe2x80x2 of the sample deformation rate is the difference between the apparent sample deformation rate and the sample deformation rate due to sintering shrinkage;
(C) separating a temperature range X in which sintering shrinkage dominates and a temperature range Y in which plastic deformation dominates with respect to the displacement of the green compact sample;
(D) substituting the corrected value Vxe2x80x2 of the sample volume for the sample volume V and substituting the corrected value (dh/dt)xe2x80x2 of the sample deformation rate for the sample deformation rate dh/dt in the Gent equation with respect to the temperature range X in which sintering shrinkage dominates; and
(E) substituting the corrected value Vxe2x80x2 of the sample volume for the sample volume V in the Gent equation with respect to the temperature range Y in which plastic deformation dominates.
In the method for measuring the viscosity of the green compact sample in the present invention, with respect to the measurement of viscosity which has been conventionally applied only to an incompressible fluid, such as a bulk sample, by executing (A) a step of extracting the corrected value Vxe2x80x2 of the sample volume by correcting the sample volume, (B) a step of extracting the corrected value (dh/dt)xe2x80x2 of the sample deformation rate by correcting the sample deformation rate, and (C) a step of separating the temperature range X in which sintering shrinkage dominates and the temperature range Y in which plastic deformation dominates with respect to the displacement of the green compact sample, and further by executing, in the Gent equation, (D) correction of the sample volume and correction of the sample deformation rate in the temperature range X in which sintering shrinkage dominates, and (E) correction of the sample volume in the temperature range Y in which plastic deformation dominates, the viscosity of the green compact sample which exhibits viscous behavior which is very close to that in the powder sate can be measured with high accuracy.
In another aspect of the present invention, in an apparatus for measuring the viscosity of a green compact sample, the viscosity xcex7 of a green compact sample formed by compaction molding of inorganic powder is measured in accordance with the Gent equation:
xcex7=2xcfx80MGH5/{3V(dh/dt)(2xcfx80H3+V)}
where M is the load, H is the height of a sample, G is the gravitational acceleration, V is the sample volume, and dh/dt is the sample deformation rate.
The apparatus includes:
(a) a sample shape measuring unit for measuring actual shape values of the green compact sample;
(b) a sample deformation rate measuring unit for measuring the apparent sample deformation rate of the green compact sample;
(c) an arithmetic processing unit for calculating the volume occupied by the inorganic powder in the green compact sample based on the actual shape values of the green compact sample and for outputting a sample volume corrected value Vxe2x80x2;
(d) an arithmetic processing unit for calculating the difference between the apparent sample deformation rate and the sample deformation rate due to sintering shrinkage of the green compact sample and for outputting a sample deformation rate corrected value (dh/dt)xe2x80x2 of the green compact sample;
(e) an arithmetic processing unit for plotting a boundary temperature between a temperature range X in which sintering shrinkage dominates and a temperature range Y in which plastic deformation dominates with respect to the displacement of the green compact sample;
(f) an arithmetic processing unit for outputting the viscosity xcex7 in the temperature range X by substituting the sample volume corrected value Vxe2x80x2 for the sample volume V and by substituting the sample deformation rate corrected value (dh/dt)xe2x80x2 for the sample deformation rate dh/dt in the Gent equation with respect to the temperature range X in which sintering shrinkage dominates;
(g) an arithmetic processing unit for outputting the viscosity xcex7 in the temperature range Y by substituting the sample volume corrected value Vxe2x80x2 for the sample volume V in the Gent equation with respect to the temperature range Y in which plastic deformation dominates; and
(h) a display for displaying the viscosity xcex7 in the temperature range X and the viscosity xcex7 in the temperature range Y.
In the apparatus for measuring the viscosity of the green compact sample in the present invention, since the apparatus includes (a) the sample shape measuring unit and (b) the sample deformation rate measuring unit, the individual arithmetic processing units (c) for the extraction of the sample volume corrected value Vxe2x80x2 by correcting the sample shape, (d) for the extraction of the sample deformation rate corrected value (dh/dt)xe2x80x2 by correcting the sample deformation rate, (e) for separating the temperature range X in which sintering shrinkage dominates and the temperature range Y in which plastic deformation dominates, (f) for correcting the sample volume and the sample deformation rate in the Gent equation with respect to the temperature range X in which sintering shrinkage dominates, and (g) for correcting the sample volume in the Gent equation with respect to the temperature range Y in which plastic deformation dominates, and (h) the display for displaying the results of the arithmetic processes, i.e., the viscosity xcex7 of the green compact sample in each temperature range, it is possible to efficiently measure the viscosity of the green compact sample which exhibits viscous behavior very close to that in the powder state by using the Gent equation which has been conventionally applicable only to an incompressible fluid, such as a bulk sample.
In another aspect of the present invention, a computer readable recording medium for storing the method for measuring the viscosity of a green compact sample is provided with a program for executing the method for measuring the viscosity of the green compact sample in the present invention.
Since the computer readable recording medium for storing the method for measuring the viscosity of the green compact sample in the present invention is provided with the program for executing the method for measuring the viscosity of the green compact sample in the present invention, it is possible to store the method for measuring viscosity of the green compact sample in the present invention and to easily transfer the technology thereof, facilitating the use thereof by many people.
In another aspect of the present invention, in a method for measuring the viscosity of a green compact sample in which the viscosity xcex7 of a green compact sample formed by compaction molding of inorganic powder is measured in accordance with the Gent equation:
xcex7=290 MGH5/{3V(dh/dt)(2xcfx80H3+V)}
where M is the load, H is the height of the sample, G is the gravitational acceleration, V is the sample volume, and dh/dt is the sample deformation rate, the measurement is performed using the green compact sample which is preliminarily calcined.
In the method for measuring the viscosity of the green compact sample, by preliminarily calcining the green compact sample, particles of the inorganic powder are sufficiently brought into close contact with each other (necked), and the viscous behavior thereof becomes very close to that of an incompressible fluid, and thus it is possible to measure the viscosity with high accuracy with respect to the green compact sample which exhibits viscous behavior that is very close to that of the inorganic powder in the powder state.